In the 20Hz waveform, the low frequency elements are being attenuated. I don't know what the lower cut-off is supposed to be. This might be normal, or a sign an AC coupliing capacitor is failing, since it does appear as though the lower frequencies are being attenuated a little more than I'd expect, going by the waveforms I get when putting a 20Hz square wave through different low pass filters in the LTSpice simulator.
What's the setting on the bass control? Does setting it to the maximum help?
What does the other channel's outout look like with a 20Hz square wave on the input?
The 1kHz waveform is fine.
At 20kHz, there's some slew rate distortion and loss of high frequency content. Your 20kHz square wave is not just 20kHz. It has much higher frequency harmonics: 30kHz, 40kHz etc. Your amplifier can't handle the fast rise and fall times of the square wave, hence why they show as diagonal lines on the trace and the edges are rounded. This is normal. It's amplifying the 20kHz component properly.
I'll post some simulated waveforms later.